Ask a Game Dev

Distilling a few semesters of upper division university math into a single blog post is kind of hard, but I’ll give it my best shot. IK is short for Inverse Kinematics, so we’ll start with that.

Kinematics is the branch of mechanics that describes motion without considering force. It describes what happens when you hold your wrist and fingers still and then move your elbow. Your wrists, forearm, and fingers all move without any application of force on them directly, because they’re inheriting the motion from your elbow. Your elbow moves and all of the parts of your body that are attached to it move with it.

Inverse Kinematics is starting from the extremities and then working our way backward. If our foot gets placed on a solid object (like a stair step), it cannot go any further. This places a constraint on the bones further up in the hierarchy - our ankle can’t move because our foot can’t move, our knee can’t move because our ankle can’t move, and our hip can’t move because our knee can’t move. Each of these joints has an maximum range of motion, so by enforcing these ranges of motion as we go up the hierarchy, we end up with a legitimate pose for the skeleton where the foot cannot penetrate the stair step.

The math comes in when we’re figuring out the position and orientation for each of our bones. Our foot bone has a set transformation because we know it can’t move any farther than where it collided with the stair step. The ankle bone exists somewhere relative to the foot bone and has built constraints for how far and what angles it can move (e.g. a normal ankle can’t bend more than maybe 150 degrees in any direction), so we can figure out where the ankle should be relative to the foot bone. From there, we continue to go up the chain to the knee bone which has a position relative to the ankle bone that will inherit the new ankle bone position and take the knee bone’s set of constraints into account (e.g. knees can’t bend more than 180 degrees). The knee bone is connected to the hip bone, the hip bone is connected to the base of the spine, and so on up until the bone you’re supposed to move doesn’t need to move because everything under it is within the hierarchy constraints.

The IK math comes in when using these constraints and expected transformations relative to the child bone’s transform to calculate the transforms for bones further up in the hierarchy, until the displacement transformation from the foot not being able to step through the stair step is distributed among the bones constraints. In principle, we’re distributing the spatial difference between where we want the foot bone to be and where the foot bone has to be across all of the bones above it in the hierarchy - the ankle, knee, hip, etc.

[Join us on Discord]

The FANTa Project is currently on hiatus while I am crunching at work too busy.

[What is the FANTa project?] [Git the FANTa Project]

Got a burning question you want answered?